A Gleason-type theorem for qubits based on mixtures of projective measurements

Victoria J Wright; Stefan Weigert

doi:10.1088/1751-8121/aaf93d

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arXiv · 1808.08091

A Gleason-type theorem for qubits based on mixtures of projective measurements

Victoria J Wright·Stefan Weigert

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Abstract

We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger. Our extension of Gleason's theorem only relies upon the consistent assignment of probabilities to the outcomes of projective measurements and their classical mixtures. This assumption is significantly weaker than those required for existing Gleason-type theorems valid in dimension two.

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Victoria J Wright, Stefan Weigert. 2018-08-24. A Gleason-type theorem for qubits based on mixtures of projective measurements. https://doi.org/10.1088/1751-8121/aaf93d

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